Question

a uniform round Board of mass M and radius R is placed on a fixed smooth horizontal plane and is free to rotate about an Axis which passes through its Centre. a Man a man of mass M is standing on the point on the circumference of the board at the first board and men are at rest the man starts moving along the rim of the board at constant speed V not relative to the board find the angle of boats rotation with them and passes his starting point on the disk first time

Answer 1

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Answer 2

The angle of boats rotation with them and passes his starting point on the disk first time 2π × (m/M) rad

Explanation:

Let the man with speed of v₀

On applying conservation of momentum, we get,

v = v₀ (m/M)

The angular rotation is given by the formula:

ω = u/R

Time taken by man to complete one revolution is:

t = 2πR/v₀

The angle is given by the formula:

θ = ωt

On substituting the formula, we get,

θ = u/R × 2πR/v₀

θ = 2π × u/v₀

∴ θ = 2π × (m/M) rad